Trotterization (and its alternative variants [1]}, [2]}, [3]}, [4]}, [5]}) provides a simple approach to digital quantum simulation and is so far the only known approach that can exploit the commutativity of the Hamiltonian. Indeed, in the extreme case where all the terms in the Hamiltonian commute, we can simultaneously diagonalize them and apply the first-order Lie-Trotter formula \({S}_1(t)\)  without error. Previous studies have also established commutator error bounds for certain low-order formulas [6]} and specific systems [7]}, [8]}. An analysis of a general formula \({S}_p(t)\)  is, however, considerably more difficult and has remained elusive until the recent proof of the commutator scaling of Trotter error [1]}.
